# Wavelet Radiosity

Peter Schröder, Steven J. Gortler, Michael Cohen, and Pat Hanrahan, Proceedings of SIGGRAPH 93

## Abstract

Radiosity methods have been shown to be an effective means to solve
the global illumination problem in Lambertian diffuse environments.
These methods approximate the radiosity integral equation by
projecting the unknown radiosity function into a set of basis
functions with limited support resulting in a set of $n$ linear
equations where $n$ is the number of discrete elements in the scene.
Classical radiosity methods required the evaluation of $n^2$
interaction coefficients. Efforts to reduce the number of required
coefficients without compromising error bounds have focused on raising
the order of the basis functions, meshing, accounting for
discontinuities, and on developing hierarchical approaches, which have
been shown to reduce the required interactions to $O(n)$.
In this paper we show that the hierarchical radiosity formulation is
an instance of a more general set of methods based on {\em wavelet\/}
theory. This general framework offers a unified view of both higher
order element approaches to radiosity and the hierarchical radiosity
methods. After a discussion of the relevant theory, we discuss a new
set of linear time hierarchical algorithms based on wavelets such as
the multiwavelet family and a flatlet basis which we introduce.
Initial results of experimentation with these basis sets are
demonstrated and discussed.

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